Question

Math

Posted 2 months ago

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$\overleftrightarrow{A B}$ and $\overleftrightarrow{C D}$ are parallel lines
Which translation of the plane can we use to prove angles $x$ and $y$ are congruent, and why?
Choose 1 answer:
(A) A translation along the directed line segment $C B$ maps line $\overleftrightarrow{C D}$ onto line $\overleftrightarrow{A B}$ and angle $y$ onto angle $x$.
(B) A translation along the directed line segment $A C$ maps line $\overleftrightarrow{A B}$ onto line $\overleftrightarrow{C D}$ and angle $x$ onto angle $y$.
C) A translation along the directed line segment $A B$ maps line $\overleftrightarrow{C D}$ onto line $\overleftrightarrow{A B}$ and angle $y$ onto angle $x$
```

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Answer from Sia

Posted 2 months ago

Solution by Steps

step 2

Corresponding angles are congruent if the lines are parallel and they are cut by a transversal

step 3

A translation is a transformation that slides every point of a figure the same distance in the same direction

step 4

To prove angles $x$ and $y$ are congruent using translation, we need to slide line $\overleftrightarrow{CD}$ onto line $\overleftrightarrow{AB}$ such that angle $y$ coincides with angle $x$

step 5

The translation along the directed line segment $CB$ will map line $\overleftrightarrow{CD}$ onto line $\overleftrightarrow{AB}$ and angle $y$ onto angle $x$

A

Key Concept

Translations and Corresponding Angles

Explanation

When parallel lines are cut by a transversal, corresponding angles are congruent. A translation that maps one line onto another and one angle onto another can be used to prove the congruence of those angles.

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